Simplify this expression: (3 + y) / (12 +4y)

To simplify the expression:

\[
\frac{3 + y}{12 + 4y}
\]

### Step 1: Factor the denominator
The denominator \( 12 + 4y \) can be factored as follows:

\[
12 + 4y = 4(3 + y)
\]

### Step 2: Rewrite the expression
Now, rewrite the expression using the factored denominator:

\[
\frac{3 + y}{4(3 + y)}
\]

### Step 3: Simplify
Since \( 3 + y \) appears in both the numerator and denominator, they cancel out:

\[
\frac{3 + y}{4(3 + y)} = \frac{1}{4}
\]

Thus, the simplified expression is:

\[
\frac{1}{4}
\]

Let me know if you have any questions or need further details!

Here are 5 related questions:
1. How do you simplify expressions with variables in both the numerator and denominator?
2. How do you factor common terms from polynomials?
3. What happens if the terms in the numerator and denominator differ by a sign (e.g., \( y - 3 \) vs. \( 3 - y \))?
4. How do you deal with complex rational expressions involving multiple variables?
5. How do you handle cases where the denominator cannot be factored?

**Tip:** Always check for common factors in both the numerator and denominator when simplifying rational expressions!

Simplify the rational expression (3 + y) / (12 + 4y) by factoring the denominator and canceling common terms. This step-by-step guide teaches essential algebraic concepts like factoring and simplifying rational expressions. Ideal for students in Grades 7-9.

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